LMFDB - Embedded newform 5292.2.bm.a.2285.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5292,2,Mod(2285,5292)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5292, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5, 1]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("5292.2285");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5292 = 2^{2} \cdot 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5292.bm (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$42.2568327497$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} + 5 x^{14} - 17 x^{13} + 22 x^{12} - 31 x^{11} + 62 x^{10} - 52 x^{9} + 52 x^{8} + \cdots + 6561 $ x^16 - 2x^15 + 5x^14 - 17x^13 + 22x^12 - 31x^11 + 62x^10 - 52x^9 + 52x^8 - 156x^7 + 558x^6 - 837x^5 + 1782x^4 - 4131x^3 + 3645x^2 - 4374*x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 3^{6} $
Twist minimal:	no (minimal twist has level 252)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			2285.5
Root			$1.68124 + 0.416458i$ of defining polynomial
Character	$\chi$	$=$	5292.2285
Dual form			5292.2.bm.a.4625.5

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.699656 q^{5} +O(q^{10})$	$q+0.699656 q^{5} +0.265217i q^{11} +(1.13823 + 0.657156i) q^{13} +(1.86392 - 3.22840i) q^{17} +(0.382449 - 0.220807i) q^{19} +4.96463i q^{23} -4.51048 q^{25} +(0.273287 - 0.157782i) q^{29} +(4.85521 - 2.80316i) q^{31} +(-0.351124 - 0.608164i) q^{37} +(5.39354 - 9.34189i) q^{41} +(3.73131 + 6.46283i) q^{43} +(-3.50285 + 6.06712i) q^{47} +(8.51919 + 4.91856i) q^{53} +0.185561i q^{55} +(-6.73182 - 11.6598i) q^{59} +(4.89484 + 2.82604i) q^{61} +(0.796368 + 0.459783i) q^{65} +(2.97060 + 5.14523i) q^{67} -13.4323i q^{71} +(6.66182 + 3.84620i) q^{73} +(-0.698360 + 1.20959i) q^{79} +(3.72399 + 6.45014i) q^{83} +(1.30410 - 2.25877i) q^{85} +(-5.59261 - 9.68668i) q^{89} +(0.267582 - 0.154489i) q^{95} +(-9.18225 + 5.30138i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q+O(q^{10}) $ 16 * q	$ 16 q - 3 q^{13} - 9 q^{17} + 16 q^{25} - 6 q^{29} - 6 q^{31} + q^{37} + 6 q^{41} - 2 q^{43} - 18 q^{47} - 15 q^{59} - 3 q^{61} + 39 q^{65} - 7 q^{67} - q^{79} + 6 q^{85} - 21 q^{89} - 6 q^{95} - 3 q^{97}+O(q^{100}) $ 16 * q - 3 * q^13 - 9 * q^17 + 16 * q^25 - 6 * q^29 - 6 * q^31 + q^37 + 6 * q^41 - 2 * q^43 - 18 * q^47 - 15 * q^59 - 3 * q^61 + 39 * q^65 - 7 * q^67 - q^79 + 6 * q^85 - 21 * q^89 - 6 * q^95 - 3 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/5292\mathbb{Z}\right)^\times$.

$n$	$785$	$1081$	$2647$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	0.699656			0.312896			0.156448	−	0.987686i	$-0.449996\pi$
$5$	0.699656			0.312896			0.156448	+	0.987686i	$0.449996\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$		0			0
$10$		0			0
$11$			0.265217i			0.0799659i	0.999200	+	0.0399829i	$0.0127304\pi$
$11$			0.265217i			0.0799659i	−0.999200	+	0.0399829i	$0.987270\pi$
$12$		0			0
$13$	1.13823	+	0.657156i	0.315688	+	0.182262i	0.649469	−	0.760388i	$-0.274991\pi$
$13$	1.13823	+	0.657156i	0.315688	+	0.182262i	−0.333781	+	0.942651i	$0.608325\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	1.86392	−	3.22840i	0.452067	−	0.783003i	−0.546447	−	0.837493i	$-0.684020\pi$
$17$	1.86392	−	3.22840i	0.452067	−	0.783003i	0.998514	+	0.0544906i	$0.0173535\pi$
$18$		0			0
$19$	0.382449	−	0.220807i	0.0877398	−	0.0506566i	−0.455488	−	0.890242i	$-0.650535\pi$
$19$	0.382449	−	0.220807i	0.0877398	−	0.0506566i	0.543228	+	0.839585i	$0.317202\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$			4.96463i			1.03520i	0.855624	+	0.517598i	$0.173174\pi$
$23$			4.96463i			1.03520i	−0.855624	+	0.517598i	$0.826826\pi$
$24$		0			0
$25$	−4.51048			−0.902096
$26$		0			0
$27$		0			0
$28$		0			0
$29$	0.273287	−	0.157782i	0.0507480	−	0.0292994i	−0.474411	−	0.880303i	$-0.657339\pi$
$29$	0.273287	−	0.157782i	0.0507480	−	0.0292994i	0.525159	+	0.851004i	$0.324006\pi$
$30$		0			0
$31$	4.85521	−	2.80316i	0.872022	−	0.503462i	0.00400255	−	0.999992i	$-0.498726\pi$
$31$	4.85521	−	2.80316i	0.872022	−	0.503462i	0.868020	+	0.496530i	$0.165393\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−0.351124	−	0.608164i	−0.0577244	−	0.0999816i	0.835719	−	0.549157i	$-0.185051\pi$
$37$	−0.351124	−	0.608164i	−0.0577244	−	0.0999816i	−0.893444	+	0.449175i	$0.851718\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	5.39354	−	9.34189i	0.842330	−	1.45896i	−0.0455900	−	0.998960i	$-0.514517\pi$
$41$	5.39354	−	9.34189i	0.842330	−	1.45896i	0.887920	−	0.459998i	$-0.152150\pi$
$42$		0			0
$43$	3.73131	+	6.46283i	0.569020	+	0.985572i	0.996663	+	0.0816240i	$0.0260106\pi$
$43$	3.73131	+	6.46283i	0.569020	+	0.985572i	−0.427643	+	0.903948i	$0.640656\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−3.50285	+	6.06712i	−0.510943	+	0.884980i	0.488976	+	0.872297i	$0.337370\pi$
$47$	−3.50285	+	6.06712i	−0.510943	+	0.884980i	−0.999920	+	0.0126827i	$0.995963\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$		0			0
$52$		0			0
$53$	8.51919	+	4.91856i	1.17020	+	0.675616i	0.953727	−	0.300672i	$-0.0972111\pi$
$53$	8.51919	+	4.91856i	1.17020	+	0.675616i	0.216474	+	0.976288i	$0.430544\pi$
$54$		0			0
$55$			0.185561i			0.0250210i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−6.73182	−	11.6598i	−0.876408	−	1.51798i	−0.855256	−	0.518206i	$-0.826600\pi$
$59$	−6.73182	−	11.6598i	−0.876408	−	1.51798i	−0.0211522	−	0.999776i	$-0.506733\pi$
$60$		0			0
$61$	4.89484	+	2.82604i	0.626720	+	0.361837i	0.779481	−	0.626426i	$-0.215483\pi$
$61$	4.89484	+	2.82604i	0.626720	+	0.361837i	−0.152761	+	0.988263i	$0.548816\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	0.796368	+	0.459783i	0.0987773	+	0.0570291i
$66$		0			0
$67$	2.97060	+	5.14523i	0.362916	+	0.628590i	0.988439	−	0.151616i	$-0.0484477\pi$
$67$	2.97060	+	5.14523i	0.362916	+	0.628590i	−0.625523	+	0.780206i	$0.715114\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	13.4323i		−	1.59412i	−0.603900	−	0.797060i	$-0.706387\pi$
$71$		−	13.4323i		−	1.59412i	0.603900	−	0.797060i	$-0.293613\pi$
$72$		0			0
$73$	6.66182	+	3.84620i	0.779707	+	0.450164i	0.836326	−	0.548232i	$-0.184699\pi$
$73$	6.66182	+	3.84620i	0.779707	+	0.450164i	−0.0566194	+	0.998396i	$0.518032\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−0.698360	+	1.20959i	−0.0785716	+	0.136090i	−0.902634	−	0.430409i	$-0.858369\pi$
$79$	−0.698360	+	1.20959i	−0.0785716	+	0.136090i	0.824062	+	0.566499i	$0.191703\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	3.72399	+	6.45014i	0.408761	+	0.707995i	0.994751	−	0.102323i	$-0.0326276\pi$
$83$	3.72399	+	6.45014i	0.408761	+	0.707995i	−0.585990	+	0.810318i	$0.699294\pi$
$84$		0			0
$85$	1.30410	−	2.25877i	0.141450	−	0.244998i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−5.59261	−	9.68668i	−0.592815	−	1.02679i	−0.993851	−	0.110724i	$-0.964683\pi$
$89$	−5.59261	−	9.68668i	−0.592815	−	1.02679i	0.401036	−	0.916062i	$-0.368650\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$	0.267582	−	0.154489i	0.0274534	−	0.0158502i
$96$		0			0
$97$	−9.18225	+	5.30138i	−0.932316	+	0.538273i	−0.887543	−	0.460724i	$-0.847590\pi$
$97$	−9.18225	+	5.30138i	−0.932316	+	0.538273i	−0.0447729	+	0.998997i	$0.514256\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	17.5071			1.74203			0.871013	−	0.491260i	$-0.163463\pi$
$101$	17.5071			1.74203			0.871013	+	0.491260i	$0.163463\pi$
$102$		0			0
$103$			8.54219i			0.841687i	0.907133	+	0.420844i	$0.138266\pi$
$103$			8.54219i			0.841687i	−0.907133	+	0.420844i	$0.861734\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	9.09489	−	5.25093i	0.879236	−	0.507627i	0.00882940	−	0.999961i	$-0.497189\pi$
$107$	9.09489	−	5.25093i	0.879236	−	0.507627i	0.870406	+	0.492334i	$0.163856\pi$
$108$		0			0
$109$	−7.12110	+	12.3341i	−0.682078	+	1.18139i	0.292268	+	0.956337i	$0.405590\pi$
$109$	−7.12110	+	12.3341i	−0.682078	+	1.18139i	−0.974346	+	0.225057i	$0.927743\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−13.3783	−	7.72396i	−1.25852	−	0.726609i	−0.285737	−	0.958308i	$-0.592238\pi$
$113$	−13.3783	−	7.72396i	−1.25852	−	0.726609i	−0.972788	+	0.231699i	$0.925572\pi$
$114$		0			0
$115$			3.47353i			0.323908i
$116$		0			0
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	10.9297			0.993605
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−6.65406			−0.595157
$126$		0			0
$127$	21.8304			1.93713			0.968566	−	0.248758i	$-0.0800225\pi$
$127$	21.8304			1.93713			0.968566	+	0.248758i	$0.0800225\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	5.20922			0.455132			0.227566	−	0.973763i	$-0.426923\pi$
$131$	5.20922			0.455132			0.227566	+	0.973763i	$0.426923\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$		0			0
$136$		0			0
$137$		−	2.69725i		−	0.230442i	−0.993340	−	0.115221i	$-0.963242\pi$
$137$		−	2.69725i		−	0.230442i	0.993340	−	0.115221i	$-0.0367576\pi$
$138$		0			0
$139$	−10.1448	−	5.85710i	−0.860470	−	0.496793i	0.00369951	−	0.999993i	$-0.498822\pi$
$139$	−10.1448	−	5.85710i	−0.860470	−	0.496793i	−0.864170	+	0.503200i	$0.832156\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−0.174289	+	0.301877i	−0.0145748	+	0.0252442i
$144$		0			0
$145$	0.191206	−	0.110393i	0.0158788	−	0.00916765i
$146$		0			0
$147$		0			0
$148$		0			0
$149$		−	18.8280i		−	1.54245i	−0.636564	−	0.771224i	$-0.719645\pi$
$149$		−	18.8280i		−	1.54245i	0.636564	−	0.771224i	$-0.280355\pi$
$150$		0			0
$151$	10.0029			0.814021			0.407010	−	0.913424i	$-0.366571\pi$
$151$	10.0029			0.814021			0.407010	+	0.913424i	$0.366571\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	3.39698	−	1.96125i	0.272852	−	0.157531i
$156$		0			0
$157$	0.218293	−	0.126032i	0.0174217	−	0.0100584i	−0.491264	−	0.871011i	$-0.663465\pi$
$157$	0.218293	−	0.126032i	0.0174217	−	0.0100584i	0.508686	+	0.860952i	$0.330132\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$		0			0
$163$	4.29780	+	7.44400i	0.336629	+	0.583059i	0.983796	−	0.179289i	$-0.0573797\pi$
$163$	4.29780	+	7.44400i	0.336629	+	0.583059i	−0.647167	+	0.762348i	$0.724046\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−2.24437	+	3.88736i	−0.173674	+	0.300813i	−0.939702	−	0.341995i	$-0.888897\pi$
$167$	−2.24437	+	3.88736i	−0.173674	+	0.300813i	0.766027	+	0.642808i	$0.222231\pi$
$168$		0			0
$169$	−5.63629	−	9.76234i	−0.433561	−	0.750949i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−3.56072	+	6.16736i	−0.270717	+	0.468895i	−0.969046	−	0.246882i	$-0.920594\pi$
$173$	−3.56072	+	6.16736i	−0.270717	+	0.468895i	0.698329	+	0.715777i	$0.253927\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		0			0
$178$		0			0
$179$	22.1270	+	12.7750i	1.65385	+	0.954848i	0.975470	+	0.220134i	$0.0706494\pi$
$179$	22.1270	+	12.7750i	1.65385	+	0.954848i	0.678376	+	0.734715i	$0.262684\pi$
$180$		0			0
$181$			0.943175i			0.0701057i	0.999385	+	0.0350528i	$0.0111599\pi$
$181$			0.943175i			0.0701057i	−0.999385	+	0.0350528i	$0.988840\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−0.245666	−	0.425506i	−0.0180617	−	0.0312838i
$186$		0			0
$187$	0.856227	+	0.494343i	0.0626135	+	0.0361499i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	2.57413	+	1.48617i	0.186258	+	0.107536i	0.590229	−	0.807236i	$-0.299037\pi$
$191$	2.57413	+	1.48617i	0.186258	+	0.107536i	−0.403972	+	0.914771i	$0.632371\pi$
$192$		0			0
$193$	9.25721	+	16.0340i	0.666348	+	1.15415i	0.978918	+	0.204254i	$0.0654769\pi$
$193$	9.25721	+	16.0340i	0.666348	+	1.15415i	−0.312570	+	0.949895i	$0.601190\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	14.1774i		−	1.01010i	−0.863091	−	0.505048i	$-0.831475\pi$
$197$		−	14.1774i		−	1.01010i	0.863091	−	0.505048i	$-0.168525\pi$
$198$		0			0
$199$	20.5293	+	11.8526i	1.45529	+	0.840209i	0.998774	−	0.0495081i	$-0.0157654\pi$
$199$	20.5293	+	11.8526i	1.45529	+	0.840209i	0.456512	+	0.889717i	$0.349099\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$		0			0
$204$		0			0
$205$	3.77362	−	6.53611i	0.263561	−	0.456502i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	0.0585617	+	0.101432i	0.00405080	+	0.00701619i
$210$		0			0
$211$	3.04004	−	5.26550i	0.209285	−	0.362492i	−0.742205	−	0.670173i	$-0.766220\pi$
$211$	3.04004	−	5.26550i	0.209285	−	0.362492i	0.951489	+	0.307681i	$0.0995531\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	2.61063	+	4.52175i	0.178044	+	0.308381i
$216$		0			0
$217$		0			0
$218$		0			0
$219$		0			0
$220$		0			0
$221$	4.24313	−	2.44977i	0.285424	−	0.164790i
$222$		0			0
$223$	0.796137	−	0.459650i	0.0533133	−	0.0307804i	−0.473106	−	0.881005i	$-0.656867\pi$
$223$	0.796137	−	0.459650i	0.0533133	−	0.0307804i	0.526420	+	0.850225i	$0.323534\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	10.0059			0.664118			0.332059	−	0.943259i	$-0.392257\pi$
$227$	10.0059			0.664118			0.332059	+	0.943259i	$0.392257\pi$
$228$		0			0
$229$		−	2.75025i		−	0.181742i	−0.995863	−	0.0908710i	$-0.971035\pi$
$229$		−	2.75025i		−	0.181742i	0.995863	−	0.0908710i	$-0.0289651\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−5.55513	+	3.20725i	−0.363928	+	0.210114i	−0.670803	−	0.741636i	$-0.734050\pi$
$233$	−5.55513	+	3.20725i	−0.363928	+	0.210114i	0.306874	+	0.951750i	$0.400717\pi$
$234$		0			0
$235$	−2.45079	+	4.24489i	−0.159872	+	0.276906i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	11.4288	+	6.59844i	0.739270	+	0.426818i	0.821804	−	0.569770i	$-0.192968\pi$
$239$	11.4288	+	6.59844i	0.739270	+	0.426818i	−0.0825337	+	0.996588i	$0.526301\pi$
$240$		0			0
$241$			2.54868i			0.164175i	0.996625	+	0.0820874i	$0.0261587\pi$
$241$			2.54868i			0.164175i	−0.996625	+	0.0820874i	$0.973841\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$		0			0
$246$		0			0
$247$	0.580418			0.0369311
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−18.7893			−1.18597			−0.592986	−	0.805213i	$-0.702051\pi$
$251$	−18.7893			−1.18597			−0.592986	+	0.805213i	$0.702051\pi$
$252$		0			0
$253$	−1.31670			−0.0827804
$254$		0			0
$255$		0			0
$256$		0			0
$257$	14.3945			0.897907			0.448953	−	0.893555i	$-0.351797\pi$
$257$	14.3945			0.897907			0.448953	+	0.893555i	$0.351797\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$		0			0
$262$		0			0
$263$			7.84976i			0.484037i	0.970272	+	0.242019i	$0.0778095\pi$
$263$			7.84976i			0.484037i	−0.970272	+	0.242019i	$0.922190\pi$
$264$		0			0
$265$	5.96050	+	3.44130i	0.366151	+	0.211397i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	7.72267	−	13.3760i	0.470859	−	0.815552i	−0.528585	−	0.848880i	$-0.677277\pi$
$269$	7.72267	−	13.3760i	0.470859	−	0.815552i	0.999444	+	0.0333281i	$0.0106106\pi$
$270$		0			0
$271$	−10.9476	+	6.32057i	−0.665016	+	0.383947i	−0.794186	−	0.607675i	$-0.792102\pi$
$271$	−10.9476	+	6.32057i	−0.665016	+	0.383947i	0.129169	+	0.991623i	$0.458769\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		−	1.19626i		−	0.0721369i
$276$		0			0
$277$	−11.8906			−0.714439			−0.357219	−	0.934021i	$-0.616275\pi$
$277$	−11.8906			−0.714439			−0.357219	+	0.934021i	$0.616275\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	2.75411	−	1.59009i	0.164297	−	0.0948568i	−0.415597	−	0.909549i	$-0.636427\pi$
$281$	2.75411	−	1.59009i	0.164297	−	0.0948568i	0.579894	+	0.814692i	$0.303094\pi$
$282$		0			0
$283$	16.0195	−	9.24889i	0.952263	−	0.549789i	0.0584799	−	0.998289i	$-0.481375\pi$
$283$	16.0195	−	9.24889i	0.952263	−	0.549789i	0.893783	+	0.448499i	$0.148041\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$		0			0
$289$	1.55161	+	2.68746i	0.0912711	+	0.158086i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	1.42975	−	2.47639i	0.0835266	−	0.144672i	−0.821236	−	0.570589i	$-0.806715\pi$
$293$	1.42975	−	2.47639i	0.0835266	−	0.144672i	0.904762	+	0.425917i	$0.140048\pi$
$294$		0			0
$295$	−4.70995	−	8.15788i	−0.274224	−	0.474970i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−3.26254	+	5.65088i	−0.188677	+	0.326799i
$300$		0			0
$301$		0			0
$302$		0			0
$303$		0			0
$304$		0			0
$305$	3.42470	+	1.97725i	0.196098	+	0.113217i
$306$		0			0
$307$		−	21.6746i		−	1.23704i	−0.785771	−	0.618518i	$-0.787734\pi$
$307$		−	21.6746i		−	1.23704i	0.785771	−	0.618518i	$-0.212266\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−11.8462	−	20.5183i	−0.671738	−	1.16348i	−0.977411	−	0.211348i	$-0.932215\pi$
$311$	−11.8462	−	20.5183i	−0.671738	−	1.16348i	0.305673	−	0.952136i	$-0.401119\pi$
$312$		0			0
$313$	−23.6283	−	13.6418i	−1.33555	−	0.771081i	−0.349407	−	0.936971i	$-0.613617\pi$
$313$	−23.6283	−	13.6418i	−1.33555	−	0.771081i	−0.986144	+	0.165890i	$0.946950\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	21.2647	+	12.2772i	1.19435	+	0.689556i	0.959289	−	0.282426i	$-0.0911391\pi$
$317$	21.2647	+	12.2772i	1.19435	+	0.689556i	0.235057	+	0.971982i	$0.424472\pi$
$318$		0			0
$319$	0.0418465	+	0.0724802i	0.00234295	+	0.00405811i
$320$		0			0
$321$		0			0
$322$		0			0
$323$		−	1.64626i		−	0.0916006i
$324$		0			0
$325$	−5.13396	−	2.96409i	−0.284781	−	0.164418i
$326$		0			0
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−8.15579	+	14.1262i	−0.448283	+	0.776449i	−0.998274	−	0.0587215i	$-0.981298\pi$
$331$	−8.15579	+	14.1262i	−0.448283	+	0.776449i	0.549991	+	0.835170i	$0.314631\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	2.07840	+	3.59989i	0.113555	+	0.196683i
$336$		0			0
$337$	13.6580	−	23.6563i	0.743998	−	1.28864i	−0.206663	−	0.978412i	$-0.566261\pi$
$337$	13.6580	−	23.6563i	0.743998	−	1.28864i	0.950661	−	0.310230i	$-0.100406\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	0.743445	+	1.28768i	0.0402598	+	0.0697320i
$342$		0			0
$343$		0			0
$344$		0			0
$345$		0			0
$346$		0			0
$347$	5.37986	−	3.10606i	0.288806	−	0.166742i	−0.348597	−	0.937273i	$-0.613342\pi$
$347$	5.37986	−	3.10606i	0.288806	−	0.166742i	0.637403	+	0.770530i	$0.280009\pi$
$348$		0			0
$349$	24.6529	−	14.2334i	1.31964	−	0.761896i	0.335971	−	0.941872i	$-0.390936\pi$
$349$	24.6529	−	14.2334i	1.31964	−	0.761896i	0.983671	+	0.179977i	$0.0576023\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	2.98691			0.158977			0.0794887	−	0.996836i	$-0.474671\pi$
$353$	2.98691			0.158977			0.0794887	+	0.996836i	$0.474671\pi$
$354$		0			0
$355$		−	9.39798i		−	0.498793i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−26.5977	+	15.3562i	−1.40377	+	0.810468i	−0.994777	−	0.102070i	$-0.967454\pi$
$359$	−26.5977	+	15.3562i	−1.40377	+	0.810468i	−0.408994	+	0.912537i	$0.634120\pi$
$360$		0			0
$361$	−9.40249	+	16.2856i	−0.494868	+	0.857136i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	4.66098	+	2.69102i	0.243967	+	0.140854i
$366$		0			0
$367$		−	19.0384i		−	0.993794i	−0.867809	−	0.496897i	$-0.834473\pi$
$367$		−	19.0384i		−	0.993794i	0.867809	−	0.496897i	$-0.165527\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$		0			0
$372$		0			0
$373$	4.11738			0.213190			0.106595	−	0.994303i	$-0.466005\pi$
$373$	4.11738			0.213190			0.106595	+	0.994303i	$0.466005\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	0.414750			0.0213607
$378$		0			0
$379$	−11.2436			−0.577546			−0.288773	−	0.957398i	$-0.593247\pi$
$379$	−11.2436			−0.577546			−0.288773	+	0.957398i	$0.593247\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	31.6093			1.61516			0.807580	−	0.589758i	$-0.200777\pi$
$383$	31.6093			1.61516			0.807580	+	0.589758i	$0.200777\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$		0			0
$388$		0			0
$389$			21.2485i			1.07734i	0.842516	+	0.538672i	$0.181074\pi$
$389$			21.2485i			1.07734i	−0.842516	+	0.538672i	$0.818926\pi$
$390$		0			0
$391$	16.0278	+	9.25367i	0.810562	+	0.467978i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−0.488611	+	0.846300i	−0.0245847	+	0.0425820i
$396$		0			0
$397$	−20.6927	+	11.9469i	−1.03854	+	0.599599i	−0.919419	−	0.393281i	$-0.871340\pi$
$397$	−20.6927	+	11.9469i	−1.03854	+	0.599599i	−0.119118	+	0.992880i	$0.538007\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$		−	25.4174i		−	1.26928i	−0.772806	−	0.634642i	$-0.781147\pi$
$401$		−	25.4174i		−	1.26928i	0.772806	−	0.634642i	$-0.218853\pi$
$402$		0			0
$403$	7.36845			0.367049
$404$		0			0
$405$		0			0
$406$		0			0
$407$	0.161295	−	0.0931240i	0.00799512	−	0.00461598i
$408$		0			0
$409$	19.3831	−	11.1908i	0.958433	−	0.553351i	0.0627424	−	0.998030i	$-0.480015\pi$
$409$	19.3831	−	11.1908i	0.958433	−	0.553351i	0.895690	+	0.444678i	$0.146682\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		0			0
$414$		0			0
$415$	2.60551	+	4.51288i	0.127900	+	0.221528i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−7.04181	+	12.1968i	−0.344015	+	0.595851i	−0.985174	−	0.171556i	$-0.945120\pi$
$419$	−7.04181	+	12.1968i	−0.344015	+	0.595851i	0.641159	+	0.767408i	$0.278454\pi$
$420$		0			0
$421$	8.07639	+	13.9887i	0.393619	+	0.681768i	0.992924	−	0.118753i	$-0.0378896\pi$
$421$	8.07639	+	13.9887i	0.393619	+	0.681768i	−0.599305	+	0.800521i	$0.704556\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−8.40717	+	14.5617i	−0.407808	+	0.706344i
$426$		0			0
$427$		0			0
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−7.16179	−	4.13486i	−0.344971	−	0.199169i	0.317497	−	0.948259i	$-0.397158\pi$
$431$	−7.16179	−	4.13486i	−0.344971	−	0.199169i	−0.662468	+	0.749090i	$0.730491\pi$
$432$		0			0
$433$			4.35102i			0.209097i	0.994520	+	0.104548i	$0.0333397\pi$
$433$			4.35102i			0.209097i	−0.994520	+	0.104548i	$0.966660\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	1.09622	+	1.89872i	0.0524395	+	0.0908279i
$438$		0			0
$439$	18.0200	+	10.4039i	0.860048	+	0.496549i	0.864028	−	0.503443i	$-0.167934\pi$
$439$	18.0200	+	10.4039i	0.860048	+	0.496549i	−0.00398054	+	0.999992i	$0.501267\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	26.7927	+	15.4688i	1.27296	+	0.734945i	0.975544	−	0.219803i	$-0.0705414\pi$
$443$	26.7927	+	15.4688i	1.27296	+	0.734945i	0.297417	+	0.954748i	$0.403875\pi$
$444$		0			0
$445$	−3.91290	−	6.77734i	−0.185489	−	0.321277i
$446$		0			0
$447$		0			0
$448$		0			0
$449$			20.9215i			0.987346i	0.869648	+	0.493673i	$0.164346\pi$
$449$			20.9215i			0.987346i	−0.869648	+	0.493673i	$0.835654\pi$
$450$		0			0
$451$	2.47763	+	1.43046i	0.116667	+	0.0673577i
$452$		0			0
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−1.15058	+	1.99286i	−0.0538217	+	0.0932218i	−0.891681	−	0.452664i	$-0.850474\pi$
$457$	−1.15058	+	1.99286i	−0.0538217	+	0.0932218i	0.837859	+	0.545886i	$0.183807\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−8.92497	−	15.4585i	−0.415677	−	0.719974i	0.579822	−	0.814743i	$-0.303122\pi$
$461$	−8.92497	−	15.4585i	−0.415677	−	0.719974i	−0.995499	+	0.0947688i	$0.969789\pi$
$462$		0			0
$463$	−6.24034	+	10.8086i	−0.290013	+	0.502318i	−0.973813	−	0.227353i	$-0.926993\pi$
$463$	−6.24034	+	10.8086i	−0.290013	+	0.502318i	0.683799	+	0.729670i	$0.260326\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	2.42799	+	4.20541i	0.112354	+	0.194603i	0.916719	−	0.399533i	$-0.130828\pi$
$467$	2.42799	+	4.20541i	0.112354	+	0.194603i	−0.804365	+	0.594136i	$0.797494\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−1.71405	+	0.989607i	−0.0788121	+	0.0455022i
$474$		0			0
$475$	−1.72503	+	0.995945i	−0.0791497	+	0.0456971i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	8.81084			0.402577			0.201289	−	0.979532i	$-0.435487\pi$
$479$	8.81084			0.402577			0.201289	+	0.979532i	$0.435487\pi$
$480$		0			0
$481$		−	0.922973i		−	0.0420839i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−6.42441	+	3.70914i	−0.291718	+	0.168423i
$486$		0			0
$487$	4.66185	−	8.07456i	0.211249	−	0.365893i	−0.740857	−	0.671663i	$-0.765580\pi$
$487$	4.66185	−	8.07456i	0.211249	−	0.365893i	0.952106	+	0.305770i	$0.0989137\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	26.9192	+	15.5418i	1.21485	+	0.701391i	0.963811	−	0.266587i	$-0.0858960\pi$
$491$	26.9192	+	15.5418i	1.21485	+	0.701391i	0.251034	+	0.967978i	$0.419229\pi$
$492$		0			0
$493$		−	1.17637i		−	0.0529811i
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−22.3388			−1.00002			−0.500010	−	0.866020i	$-0.666670\pi$
$499$	−22.3388			−1.00002			−0.500010	+	0.866020i	$0.666670\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	12.2396			0.545738			0.272869	−	0.962051i	$-0.412027\pi$
$503$	12.2396			0.545738			0.272869	+	0.962051i	$0.412027\pi$
$504$		0			0
$505$	12.2490			0.545072
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−14.1099			−0.625411			−0.312706	−	0.949850i	$-0.601235\pi$
$509$	−14.1099			−0.625411			−0.312706	+	0.949850i	$0.601235\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$		0			0
$514$		0			0
$515$			5.97659i			0.263360i
$516$		0			0
$517$	−1.60910	−	0.929015i	−0.0707682	−	0.0408580i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−2.81632	+	4.87800i	−0.123385	+	0.213709i	−0.921101	−	0.389325i	$-0.872708\pi$
$521$	−2.81632	+	4.87800i	−0.123385	+	0.213709i	0.797715	+	0.603034i	$0.206042\pi$
$522$		0			0
$523$	33.2293	−	19.1849i	1.45302	−	0.838899i	0.454364	−	0.890816i	$-0.349867\pi$
$523$	33.2293	−	19.1849i	1.45302	−	0.838899i	0.998651	+	0.0519176i	$0.0165333\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		−	20.8995i		−	0.910395i
$528$		0			0
$529$	−1.64754			−0.0716321
$530$		0			0
$531$		0			0
$532$		0			0
$533$	12.2782	−	7.08880i	0.531826	−	0.307050i
$534$		0			0
$535$	6.36329	−	3.67385i	0.275109	−	0.158834i
$536$		0			0
$537$		0			0
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−3.21673	−	5.57154i	−0.138298	−	0.239539i	0.788555	−	0.614965i	$-0.210830\pi$
$541$	−3.21673	−	5.57154i	−0.138298	−	0.239539i	−0.926852	+	0.375426i	$0.877496\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−4.98232	+	8.62963i	−0.213419	+	0.369653i
$546$		0			0
$547$	−6.52889	−	11.3084i	−0.279155	−	0.483511i	0.692020	−	0.721878i	$-0.256721\pi$
$547$	−6.52889	−	11.3084i	−0.279155	−	0.483511i	−0.971175	+	0.238368i	$0.923388\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	0.0696787	−	0.120687i	0.00296841	−	0.00514144i
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−25.5409	−	14.7460i	−1.08220	−	0.624809i	−0.150712	−	0.988578i	$-0.548157\pi$
$557$	−25.5409	−	14.7460i	−1.08220	−	0.624809i	−0.931489	+	0.363769i	$0.881490\pi$
$558$		0			0
$559$			9.80822i			0.414844i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−5.25934	−	9.10944i	−0.221655	−	0.383917i	0.733656	−	0.679521i	$-0.237812\pi$
$563$	−5.25934	−	9.10944i	−0.221655	−	0.383917i	−0.955311	+	0.295604i	$0.904479\pi$
$564$		0			0
$565$	−9.36020	−	5.40411i	−0.393787	−	0.227353i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	22.8054	+	13.1667i	0.956053	+	0.551977i	0.894956	−	0.446155i	$-0.147207\pi$
$569$	22.8054	+	13.1667i	0.956053	+	0.551977i	0.0610967	+	0.998132i	$0.480540\pi$
$570$		0			0
$571$	22.0295	+	38.1562i	0.921906	+	1.59679i	0.796463	+	0.604688i	$0.206702\pi$
$571$	22.0295	+	38.1562i	0.921906	+	1.59679i	0.125444	+	0.992101i	$0.459965\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		−	22.3929i		−	0.933847i
$576$		0			0
$577$	−12.1535	−	7.01684i	−0.505957	−	0.292115i	0.225213	−	0.974310i	$-0.427692\pi$
$577$	−12.1535	−	7.01684i	−0.505957	−	0.292115i	−0.731170	+	0.682195i	$0.761026\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−1.30448	+	2.25943i	−0.0540262	+	0.0935762i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−1.52469	−	2.64085i	−0.0629308	−	0.108999i	0.832843	−	0.553509i	$-0.186711\pi$
$587$	−1.52469	−	2.64085i	−0.0629308	−	0.108999i	−0.895774	+	0.444509i	$0.853378\pi$
$588$		0			0
$589$	1.23791	−	2.14413i	0.0510073	−	0.0883473i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−13.3041	−	23.0434i	−0.546334	−	0.946278i	−0.998522	−	0.0543552i	$-0.982690\pi$
$593$	−13.3041	−	23.0434i	−0.546334	−	0.946278i	0.452188	−	0.891923i	$-0.350644\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$	3.86333	−	2.23050i	0.157852	−	0.0911356i	−0.418993	−	0.907989i	$-0.637617\pi$
$599$	3.86333	−	2.23050i	0.157852	−	0.0911356i	0.576845	+	0.816854i	$0.304284\pi$
$600$		0			0
$601$	5.25019	−	3.03120i	0.214160	−	0.123645i	−0.389083	−	0.921203i	$-0.627208\pi$
$601$	5.25019	−	3.03120i	0.214160	−	0.123645i	0.603243	+	0.797557i	$0.293875\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	7.64700			0.310895
$606$		0			0
$607$			45.3313i			1.83994i	0.391986	+	0.919971i	$0.371788\pi$
$607$			45.3313i			1.83994i	−0.391986	+	0.919971i	$0.628212\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−7.97409	+	4.60384i	−0.322597	+	0.186251i
$612$		0			0
$613$	16.6294	−	28.8029i	0.671654	−	1.16334i	−0.305781	−	0.952102i	$-0.598917\pi$
$613$	16.6294	−	28.8029i	0.671654	−	1.16334i	0.977435	−	0.211237i	$-0.0677492\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−31.3001	−	18.0711i	−1.26010	−	0.727516i	−0.287002	−	0.957930i	$-0.592659\pi$
$617$	−31.3001	−	18.0711i	−1.26010	−	0.727516i	−0.973093	+	0.230414i	$0.925992\pi$
$618$		0			0
$619$			26.4462i			1.06296i	0.847069	+	0.531482i	$0.178365\pi$
$619$			26.4462i			1.06296i	−0.847069	+	0.531482i	$0.821635\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	17.8969			0.715874
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−2.61787			−0.104381
$630$		0			0
$631$	−32.0484			−1.27583			−0.637914	−	0.770107i	$-0.720203\pi$
$631$	−32.0484			−1.27583			−0.637914	+	0.770107i	$0.720203\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	15.2737			0.606120
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$		−	24.4154i		−	0.964351i	−0.876075	−	0.482176i	$-0.839847\pi$
$641$		−	24.4154i		−	0.964351i	0.876075	−	0.482176i	$-0.160153\pi$
$642$		0			0
$643$	−31.9014	−	18.4183i	−1.25807	−	0.726346i	−0.285370	−	0.958418i	$-0.592116\pi$
$643$	−31.9014	−	18.4183i	−1.25807	−	0.726346i	−0.972699	+	0.232071i	$0.925450\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−13.2847	+	23.0098i	−0.522276	+	0.904608i	0.477389	+	0.878692i	$0.341583\pi$
$647$	−13.2847	+	23.0098i	−0.522276	+	0.904608i	−0.999664	+	0.0259155i	$0.991750\pi$
$648$		0			0
$649$	3.09239	−	1.78539i	0.121387	−	0.0700827i
$650$		0			0
$651$		0			0
$652$		0			0
$653$		−	30.3418i		−	1.18737i	−0.804699	−	0.593683i	$-0.797673\pi$
$653$		−	30.3418i		−	1.18737i	0.804699	−	0.593683i	$-0.202327\pi$
$654$		0			0
$655$	3.64466			0.142409
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−40.9873	+	23.6640i	−1.59664	+	0.921820i	−0.604511	+	0.796597i	$0.706631\pi$
$659$	−40.9873	+	23.6640i	−1.59664	+	0.921820i	−0.992129	+	0.125223i	$0.960035\pi$
$660$		0			0
$661$	−30.4187	+	17.5623i	−1.18315	+	0.683092i	−0.956741	−	0.290940i	$-0.906032\pi$
$661$	−30.4187	+	17.5623i	−1.18315	+	0.683092i	−0.226409	+	0.974032i	$0.572699\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		0			0
$666$		0			0
$667$	0.783329	+	1.35677i	0.0303306	+	0.0525342i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−0.749513	+	1.29819i	−0.0289346	+	0.0501162i
$672$		0			0
$673$	−2.54758	−	4.41254i	−0.0982020	−	0.170091i	0.812738	−	0.582629i	$-0.197976\pi$
$673$	−2.54758	−	4.41254i	−0.0982020	−	0.170091i	−0.910940	+	0.412538i	$0.864642\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−8.42072	+	14.5851i	−0.323635	+	0.560551i	−0.981235	−	0.192815i	$-0.938238\pi$
$677$	−8.42072	+	14.5851i	−0.323635	+	0.560551i	0.657601	+	0.753367i	$0.271571\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$		0			0
$683$	15.7555	+	9.09645i	0.602868	+	0.348066i	0.770169	−	0.637840i	$-0.220172\pi$
$683$	15.7555	+	9.09645i	0.602868	+	0.348066i	−0.167301	+	0.985906i	$0.553505\pi$
$684$		0			0
$685$		−	1.88715i		−	0.0721042i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	6.46452	+	11.1969i	0.246279	+	0.426567i
$690$		0			0
$691$	3.05405	+	1.76326i	0.116182	+	0.0670775i	0.556965	−	0.830536i	$-0.311966\pi$
$691$	3.05405	+	1.76326i	0.116182	+	0.0670775i	−0.440783	+	0.897614i	$0.645299\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−7.09786	−	4.09795i	−0.269237	−	0.155444i
$696$		0			0
$697$	−20.1063	−	34.8251i	−0.761579	−	1.31909i
$698$		0			0
$699$		0			0
$700$		0			0
$701$		−	13.3502i		−	0.504229i	−0.967697	−	0.252114i	$-0.918874\pi$
$701$		−	13.3502i		−	0.504229i	0.967697	−	0.252114i	$-0.0811259\pi$
$702$		0			0
$703$	−0.268574	−	0.155061i	−0.0101295	−	0.00584824i
$704$		0			0
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	21.1447	−	36.6237i	0.794107	−	1.37543i	−0.129298	−	0.991606i	$-0.541273\pi$
$709$	21.1447	−	36.6237i	0.794107	−	1.37543i	0.923405	−	0.383827i	$-0.125394\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	13.9166	+	24.1043i	0.521182	+	0.902715i
$714$		0			0
$715$	−0.121942	+	0.211210i	−0.00456038	+	0.00789881i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−15.2035	−	26.3332i	−0.566994	−	0.982062i	−0.996861	−	0.0791697i	$-0.974773\pi$
$719$	−15.2035	−	26.3332i	−0.566994	−	0.982062i	0.429868	−	0.902892i	$-0.358560\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−1.23265	+	0.711673i	−0.0457796	+	0.0264309i
$726$		0			0
$727$	−11.3671	+	6.56280i	−0.421583	+	0.243401i	−0.695754	−	0.718280i	$-0.744930\pi$
$727$	−11.3671	+	6.56280i	−0.421583	+	0.243401i	0.274171	+	0.961681i	$0.411596\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	27.8195			1.02894
$732$		0			0
$733$		−	37.7588i		−	1.39465i	−0.716753	−	0.697327i	$-0.754372\pi$
$733$		−	37.7588i		−	1.39465i	0.716753	−	0.697327i	$-0.245628\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−1.36460	+	0.787853i	−0.0502657	+	0.0290209i
$738$		0			0
$739$	−13.1215	+	22.7271i	−0.482683	+	0.836031i	−0.999802	−	0.0198820i	$-0.993671\pi$
$739$	−13.1215	+	22.7271i	−0.482683	+	0.836031i	0.517119	+	0.855913i	$0.327004\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	8.78379	+	5.07132i	0.322246	+	0.186049i	0.652393	−	0.757881i	$-0.273765\pi$
$743$	8.78379	+	5.07132i	0.322246	+	0.186049i	−0.330147	+	0.943929i	$0.607098\pi$
$744$		0			0
$745$		−	13.1731i		−	0.482625i
$746$		0			0
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$	7.90737			0.288544			0.144272	−	0.989538i	$-0.453916\pi$
$751$	7.90737			0.288544			0.144272	+	0.989538i	$0.453916\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	6.99855			0.254703
$756$		0			0
$757$	29.8903			1.08638			0.543191	−	0.839609i	$-0.317216\pi$
$757$	29.8903			1.08638			0.543191	+	0.839609i	$0.317216\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−6.11374			−0.221623			−0.110811	−	0.993841i	$-0.535345\pi$
$761$	−6.11374			−0.221623			−0.110811	+	0.993841i	$0.535345\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$		−	17.6954i		−	0.638944i
$768$		0			0
$769$	−9.79863	−	5.65724i	−0.353348	−	0.204005i	0.312811	−	0.949815i	$-0.398729\pi$
$769$	−9.79863	−	5.65724i	−0.353348	−	0.204005i	−0.666159	+	0.745810i	$0.732063\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−19.2106	+	33.2737i	−0.690956	+	1.19677i	0.280569	+	0.959834i	$0.409477\pi$
$773$	−19.2106	+	33.2737i	−0.690956	+	1.19677i	−0.971525	+	0.236937i	$0.923856\pi$
$774$		0			0
$775$	−21.8994	+	12.6436i	−0.786648	+	0.454172i
$776$		0			0
$777$		0			0
$778$		0			0
$779$		−	4.76373i		−	0.170678i
$780$		0			0
$781$	3.56247			0.127475
$782$		0			0
$783$		0			0
$784$		0			0
$785$	0.152730	−	0.0881788i	0.00545117	−	0.00314723i
$786$		0			0
$787$	−41.2747	+	23.8300i	−1.47129	+	0.849447i	−0.999480	−	0.0322557i	$-0.989731\pi$
$787$	−41.2747	+	23.8300i	−1.47129	+	0.849447i	−0.471806	+	0.881703i	$0.656398\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$	3.71430	+	6.43335i	0.131898	+	0.228455i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	15.1359	−	26.2161i	0.536139	−	0.928621i	−0.462968	−	0.886375i	$-0.653215\pi$
$797$	15.1359	−	26.2161i	0.536139	−	0.928621i	0.999107	−	0.0422457i	$-0.0134512\pi$
$798$		0			0
$799$	13.0581	+	22.6172i	0.461961	+	0.800140i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−1.02008	+	1.76683i	−0.0359978	+	0.0623500i
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	0.219373	+	0.126655i	0.00771273	+	0.00445295i	0.503851	−	0.863790i	$-0.331916\pi$
$809$	0.219373	+	0.126655i	0.00771273	+	0.00445295i	−0.496139	+	0.868243i	$0.665249\pi$
$810$		0			0
$811$			22.0629i			0.774735i	0.921925	+	0.387367i	$0.126615\pi$
$811$			22.0629i			0.774735i	−0.921925	+	0.387367i	$0.873385\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	3.00698	+	5.20824i	0.105330	+	0.182437i
$816$		0			0
$817$	2.85407	+	1.64780i	0.0998514	+	0.0576492i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−24.2467	−	13.9988i	−0.846214	−	0.488562i	0.0131576	−	0.999913i	$-0.495812\pi$
$821$	−24.2467	−	13.9988i	−0.846214	−	0.488562i	−0.859372	+	0.511352i	$0.829145\pi$
$822$		0			0
$823$	−24.4771	−	42.3955i	−0.853217	−	1.47782i	−0.878289	−	0.478130i	$-0.841315\pi$
$823$	−24.4771	−	42.3955i	−0.853217	−	1.47782i	0.0250719	−	0.999686i	$-0.492019\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			0.641658i			0.0223126i	0.999938	+	0.0111563i	$0.00355124\pi$
$827$			0.641658i			0.0223126i	−0.999938	+	0.0111563i	$0.996449\pi$
$828$		0			0
$829$	−9.57180	−	5.52628i	−0.332442	−	0.191936i	0.324483	−	0.945892i	$-0.394810\pi$
$829$	−9.57180	−	5.52628i	−0.332442	−	0.191936i	−0.656925	+	0.753956i	$0.728143\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−1.57029	+	2.71981i	−0.0543420	+	0.0941230i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	4.62330	+	8.00780i	0.159614	+	0.276460i	0.934730	−	0.355360i	$-0.115642\pi$
$839$	4.62330	+	8.00780i	0.159614	+	0.276460i	−0.775115	+	0.631820i	$0.782308\pi$
$840$		0			0
$841$	−14.4502	+	25.0285i	−0.498283	+	0.863052i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−3.94346	−	6.83028i	−0.135659	−	0.234969i
$846$		0			0
$847$		0			0
$848$		0			0
$849$		0			0
$850$		0			0
$851$	3.01931	−	1.74320i	0.103501	−	0.0597561i
$852$		0			0
$853$	−34.3256	+	19.8179i	−1.17529	+	0.678551i	−0.954919	−	0.296866i	$-0.904059\pi$
$853$	−34.3256	+	19.8179i	−1.17529	+	0.678551i	−0.220366	+	0.975417i	$0.570725\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−23.8520			−0.814770			−0.407385	−	0.913256i	$-0.633559\pi$
$857$	−23.8520			−0.814770			−0.407385	+	0.913256i	$0.633559\pi$
$858$		0			0
$859$		−	11.1138i		−	0.379197i	−0.981862	−	0.189598i	$-0.939281\pi$
$859$		−	11.1138i		−	0.379197i	0.981862	−	0.189598i	$-0.0607186\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−38.7780	+	22.3885i	−1.32002	+	0.762113i	−0.983731	−	0.179646i	$-0.942505\pi$
$863$	−38.7780	+	22.3885i	−1.32002	+	0.762113i	−0.336287	+	0.941759i	$0.609171\pi$
$864$		0			0
$865$	−2.49128	+	4.31503i	−0.0847061	+	0.146715i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−0.320805	−	0.185217i	−0.0108826	−	0.00628305i
$870$		0			0
$871$			7.80859i			0.264584i
$872$		0			0
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$	3.68191			0.124329			0.0621647	−	0.998066i	$-0.480200\pi$
$877$	3.68191			0.124329			0.0621647	+	0.998066i	$0.480200\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−17.3992			−0.586194			−0.293097	−	0.956083i	$-0.594686\pi$
$881$	−17.3992			−0.586194			−0.293097	+	0.956083i	$0.594686\pi$
$882$		0			0
$883$	−2.02834			−0.0682592			−0.0341296	−	0.999417i	$-0.510866\pi$
$883$	−2.02834			−0.0682592			−0.0341296	+	0.999417i	$0.510866\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	46.3780			1.55722			0.778610	−	0.627508i	$-0.215925\pi$
$887$	46.3780			1.55722			0.778610	+	0.627508i	$0.215925\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$		0			0
$892$		0			0
$893$			3.09381i			0.103531i
$894$		0			0
$895$	15.4812	+	8.93810i	0.517481	+	0.298768i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	0.884576	−	1.53213i	0.0295023	−	0.0510994i
$900$		0			0
$901$	31.7582	−	18.3356i	1.05802	−	0.610847i
$902$		0			0
$903$		0			0
$904$		0			0
$905$			0.659898i			0.0219357i
$906$		0			0
$907$	16.0391			0.532571			0.266285	−	0.963894i	$-0.414204\pi$
$907$	16.0391			0.532571			0.266285	+	0.963894i	$0.414204\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−17.7833	+	10.2672i	−0.589187	+	0.340167i	−0.764776	−	0.644296i	$-0.777150\pi$
$911$	−17.7833	+	10.2672i	−0.589187	+	0.340167i	0.175589	+	0.984464i	$0.443817\pi$
$912$		0			0
$913$	−1.71069	+	0.987665i	−0.0566154	+	0.0326869i
$914$		0			0
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−17.7069	−	30.6693i	−0.584097	−	1.01169i	−0.994987	−	0.100001i	$-0.968115\pi$
$919$	−17.7069	−	30.6693i	−0.584097	−	1.01169i	0.410890	−	0.911685i	$-0.365218\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	8.82712	−	15.2890i	0.290548	−	0.503244i
$924$		0			0
$925$	1.58374	+	2.74311i	0.0520730	+	0.0901930i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−19.8626	+	34.4030i	−0.651670	+	1.12873i	0.331048	+	0.943614i	$0.392598\pi$
$929$	−19.8626	+	34.4030i	−0.651670	+	1.12873i	−0.982718	+	0.185111i	$0.940735\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$		0			0
$934$		0			0
$935$	0.599064	+	0.345870i	0.0195915	+	0.0113112i
$936$		0			0
$937$			23.2142i			0.758376i	0.925320	+	0.379188i	$0.123797\pi$
$937$			23.2142i			0.758376i	−0.925320	+	0.379188i	$0.876203\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−17.9616	−	31.1104i	−0.585531	−	1.01417i	−0.994809	−	0.101760i	$-0.967553\pi$
$941$	−17.9616	−	31.1104i	−0.585531	−	1.01417i	0.409278	−	0.912410i	$-0.365781\pi$
$942$		0			0
$943$	46.3790	+	26.7769i	1.51031	+	0.871977i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	26.7365	+	15.4363i	0.868818	+	0.501612i	0.866955	−	0.498386i	$-0.166074\pi$
$947$	26.7365	+	15.4363i	0.868818	+	0.501612i	0.00186277	+	0.999998i	$0.499407\pi$
$948$		0			0
$949$	5.05511	+	8.75571i	0.164096	+	0.284222i
$950$		0			0
$951$		0			0
$952$		0			0
$953$			30.4640i			0.986826i	0.869795	+	0.493413i	$0.164251\pi$
$953$			30.4640i			0.986826i	−0.869795	+	0.493413i	$0.835749\pi$
$954$		0			0
$955$	1.80100	+	1.03981i	0.0582791	+	0.0336475i
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	0.215406	−	0.373095i	0.00694859	−	0.0120353i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	6.47686	+	11.2182i	0.208497	+	0.361128i
$966$		0			0
$967$	−6.75865	+	11.7063i	−0.217343	+	0.376450i	−0.953995	−	0.299823i	$-0.903072\pi$
$967$	−6.75865	+	11.7063i	−0.217343	+	0.376450i	0.736652	+	0.676272i	$0.236406\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−16.6428	−	28.8261i	−0.534092	−	0.925074i	−0.999207	−	0.0398238i	$-0.987320\pi$
$971$	−16.6428	−	28.8261i	−0.534092	−	0.925074i	0.465115	−	0.885250i	$-0.346013\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−38.9127	+	22.4662i	−1.24493	+	0.718758i	−0.970093	−	0.242734i	$-0.921956\pi$
$977$	−38.9127	+	22.4662i	−1.24493	+	0.718758i	−0.274833	+	0.961492i	$0.588623\pi$
$978$		0			0
$979$	2.56907	−	1.48325i	0.0821079	−	0.0474050i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−26.8949			−0.857813			−0.428907	−	0.903349i	$-0.641101\pi$
$983$	−26.8949			−0.857813			−0.428907	+	0.903349i	$0.641101\pi$
$984$		0			0
$985$		−	9.91929i		−	0.316055i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−32.0855	+	18.5246i	−1.02026	+	0.589048i
$990$		0			0
$991$	17.7201	−	30.6920i	0.562896	−	0.974965i	−0.434346	−	0.900746i	$-0.643020\pi$
$991$	17.7201	−	30.6920i	0.562896	−	0.974965i	0.997242	−	0.0742186i	$-0.0236463\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	14.3635	+	8.29275i	0.455352	+	0.262898i
$996$		0			0
$997$			32.4953i			1.02914i	0.857449	+	0.514568i	$0.172048\pi$
$997$			32.4953i			1.02914i	−0.857449	+	0.514568i	$0.827952\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5292.2.bm.a.2285.5		16
3.2	odd	2		1764.2.bm.a.1697.1		16
7.2	even	3		756.2.w.a.341.4		16
7.3	odd	6		5292.2.x.b.881.5		16
7.4	even	3		5292.2.x.a.881.4		16
7.5	odd	6		5292.2.w.b.1097.5		16
7.6	odd	2		756.2.bm.a.17.4		16
9.2	odd	6		5292.2.w.b.521.5		16
9.7	even	3		1764.2.w.b.1109.3		16
21.2	odd	6		252.2.w.a.5.6	✓	16
21.5	even	6		1764.2.w.b.509.3		16
21.11	odd	6		1764.2.x.a.293.6		16
21.17	even	6		1764.2.x.b.293.3		16
21.20	even	2		252.2.bm.a.185.8	yes	16
28.23	odd	6		3024.2.ca.d.2609.4		16
28.27	even	2		3024.2.df.d.17.4		16
63.2	odd	6		756.2.bm.a.89.4		16
63.11	odd	6		5292.2.x.b.4409.5		16
63.13	odd	6		2268.2.t.b.1781.5		16
63.16	even	3		252.2.bm.a.173.8	yes	16
63.20	even	6		756.2.w.a.521.4		16
63.23	odd	6		2268.2.t.b.2105.5		16
63.25	even	3		1764.2.x.b.1469.3		16
63.34	odd	6		252.2.w.a.101.6	yes	16
63.38	even	6		5292.2.x.a.4409.4		16
63.41	even	6		2268.2.t.a.1781.4		16
63.47	even	6	inner	5292.2.bm.a.4625.5		16
63.52	odd	6		1764.2.x.a.1469.6		16
63.58	even	3		2268.2.t.a.2105.4		16
63.61	odd	6		1764.2.bm.a.1685.1		16
84.23	even	6		1008.2.ca.d.257.3		16
84.83	odd	2		1008.2.df.d.689.1		16
252.79	odd	6		1008.2.df.d.929.1		16
252.83	odd	6		3024.2.ca.d.2033.4		16
252.191	even	6		3024.2.df.d.1601.4		16
252.223	even	6		1008.2.ca.d.353.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.w.a.5.6	✓	16	21.2	odd	6
252.2.w.a.101.6	yes	16	63.34	odd	6
252.2.bm.a.173.8	yes	16	63.16	even	3
252.2.bm.a.185.8	yes	16	21.20	even	2
756.2.w.a.341.4		16	7.2	even	3
756.2.w.a.521.4		16	63.20	even	6
756.2.bm.a.17.4		16	7.6	odd	2
756.2.bm.a.89.4		16	63.2	odd	6
1008.2.ca.d.257.3		16	84.23	even	6
1008.2.ca.d.353.3		16	252.223	even	6
1008.2.df.d.689.1		16	84.83	odd	2
1008.2.df.d.929.1		16	252.79	odd	6
1764.2.w.b.509.3		16	21.5	even	6
1764.2.w.b.1109.3		16	9.7	even	3
1764.2.x.a.293.6		16	21.11	odd	6
1764.2.x.a.1469.6		16	63.52	odd	6
1764.2.x.b.293.3		16	21.17	even	6
1764.2.x.b.1469.3		16	63.25	even	3
1764.2.bm.a.1685.1		16	63.61	odd	6
1764.2.bm.a.1697.1		16	3.2	odd	2
2268.2.t.a.1781.4		16	63.41	even	6
2268.2.t.a.2105.4		16	63.58	even	3
2268.2.t.b.1781.5		16	63.13	odd	6
2268.2.t.b.2105.5		16	63.23	odd	6
3024.2.ca.d.2033.4		16	252.83	odd	6
3024.2.ca.d.2609.4		16	28.23	odd	6
3024.2.df.d.17.4		16	28.27	even	2
3024.2.df.d.1601.4		16	252.191	even	6
5292.2.w.b.521.5		16	9.2	odd	6
5292.2.w.b.1097.5		16	7.5	odd	6
5292.2.x.a.881.4		16	7.4	even	3
5292.2.x.a.4409.4		16	63.38	even	6
5292.2.x.b.881.5		16	7.3	odd	6
5292.2.x.b.4409.5		16	63.11	odd	6
5292.2.bm.a.2285.5		16	1.1	even	1	trivial
5292.2.bm.a.4625.5		16	63.47	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 5292 = 2^{2} \cdot 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5292.bm (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+0.699656 q^{5} +O(q^{10})\)	\(q+0.699656 q^{5} +0.265217i q^{11} +(1.13823 + 0.657156i) q^{13} +(1.86392 - 3.22840i) q^{17} +(0.382449 - 0.220807i) q^{19} +4.96463i q^{23} -4.51048 q^{25} +(0.273287 - 0.157782i) q^{29} +(4.85521 - 2.80316i) q^{31} +(-0.351124 - 0.608164i) q^{37} +(5.39354 - 9.34189i) q^{41} +(3.73131 + 6.46283i) q^{43} +(-3.50285 + 6.06712i) q^{47} +(8.51919 + 4.91856i) q^{53} +0.185561i q^{55} +(-6.73182 - 11.6598i) q^{59} +(4.89484 + 2.82604i) q^{61} +(0.796368 + 0.459783i) q^{65} +(2.97060 + 5.14523i) q^{67} -13.4323i q^{71} +(6.66182 + 3.84620i) q^{73} +(-0.698360 + 1.20959i) q^{79} +(3.72399 + 6.45014i) q^{83} +(1.30410 - 2.25877i) q^{85} +(-5.59261 - 9.68668i) q^{89} +(0.267582 - 0.154489i) q^{95} +(-9.18225 + 5.30138i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q+O(q^{10}) \) 16 * q	\( 16 q - 3 q^{13} - 9 q^{17} + 16 q^{25} - 6 q^{29} - 6 q^{31} + q^{37} + 6 q^{41} - 2 q^{43} - 18 q^{47} - 15 q^{59} - 3 q^{61} + 39 q^{65} - 7 q^{67} - q^{79} + 6 q^{85} - 21 q^{89} - 6 q^{95} - 3 q^{97}+O(q^{100}) \) 16 * q - 3 * q^13 - 9 * q^17 + 16 * q^25 - 6 * q^29 - 6 * q^31 + q^37 + 6 * q^41 - 2 * q^43 - 18 * q^47 - 15 * q^59 - 3 * q^61 + 39 * q^65 - 7 * q^67 - q^79 + 6 * q^85 - 21 * q^89 - 6 * q^95 - 3 * q^97

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